摘要
在机器人研究领域中，机器视觉、听觉、触觉和力觉的研究都取得了相当多的成果，有的已达到实用的水准。机器味觉和嗅觉在食品加工业的企业管理、产品质量的检测、口味和味道的评定等领域有着广泛的应用，但机器味觉和嗅觉研究的进展却一直较为缓慢，因为机器味觉和嗅觉的实现，一方面要求研制出高灵敏度的味觉和嗅觉传感器，另一方面还要求有性能良好的模式识别系统。自20世纪80年代末，日本的许多科学家开始致力于味觉和嗅觉传感器的研究，目前不仅成功提取出“酸、甜、苦、香、咸”五种基本味觉，对于食物和饮料，如：米饭、矿泉水和啤酒等味觉信号的提取和量化也取得了一定的进展。
同时，快速而有效地确定神经网络的结构和参数一直是神经元网络研究的难点，目前解决这一问题的基本思路是从研究的数据中提取知识，然后再利用提取的知识指导神经网络的构建，如模糊神经网络的实现。利用贝叶斯概率理论方法指导神经网络结构及粒子群优化算法(ParticleSwarm Optimization，以下简称PSO)调整神经网络参数，作为两种独立的方法目前都已取得了一些成果。
本文提出了一种新的最小不确定性神经网络模型(Minimal UncertaintyNeural Networks)，该模型基于最小不确定性判决确定神经网络结构。
定理1：设有N维输入向量X={x_1,X_2，…，x_N)，各属性x_1，x_2，…x_N两两相互独立，令P(K)为事件K出现的概率，称π=1-P(y|X)为给定X下对y的不确定性，则有π=multiply from i=1 to N(1-p(y|x_1))。
推论1：当给定分类集Y=(y_1，y_2…，yM)且j∈[1，2，…，M]时，可得给定X下对各类yj的不确定性为：π_j=1-P(y_j|X)=multiply from i=1 to N(1-P(y_j|x_i))。由此，当分类时选择不确定性最小的π_j作为最终判决，定义为最小不确定性判决。
定义最小不确定性神经网络模型(MUNN)为：S_j=logπ_j，β_j=N log P(y+j)，
中文摘要
，1一P(y，lx，，.)、，，、‘.一‘---...一
鸟=109(‘蓄兴二)，凡一o，=f(s，)二“xp’，。神经网络结构如图1所示。各
P(为)‘”’一’一’“，，一~『‘刁一“分目‘.，州目“z’‘“’。目
层含义如下:
[A1层:样本输入层，A为观测值，x，i’为属性x‘的观测值。
[B]层:权值选择层，二‘t’EA时，Ot，，=1;否则，Oi，，二0o
[C]层:加权计算层，由(l .4)式得到s’。
[Dl层:不确定性输出层，由(l .7)或(l .8)式得到呀输出
fD7
fCI(二，l)(:12)(二2，)(:22
fB]r全二se一鉴
fAZ!才={…x。，…}，化〔l川
图1:一个简单的二属性输入两类判别的最小不确定性神经网(此处N=2)
结合贝叶斯概率和粒子群优化算法(PSO)对其参数进行训练。
在使用贝叶斯概率训练最小不确定性神经网络时，我们首先进行一个统
计过程国:c·工k‘尹，，ci，一艺k‘”吞，·“，，。，，，*一艺k‘·，瓷‘.‘·，易.‘·，
r尸产
其中r为输入样本在训练集的位置，与，.(r)代表属性:，(r)的值xti，，劲，(r)
代表属性沪的值为，，洲为输入属性的权重，一般取1。于是推导出如下
权值及阐值的表达式:
鸟二109
((ci+a/叹)一(马+a/(伙礼))(C+a))
(ci+a/乓)(cj+a/mz)
几二N fog
马+a/m，
C+C
a一般取很小的数，在后面的试验中我们将a设为1/C，使其误差
澎1091/CZ幽
中文摘要
利用Pso训练时，我们直接将最小不确定性神经网模型中的权值马及
闽值几作为粒子的参数，错误分类的数目作为粒子的适应值，利用Pso迭
代公式:
v(t+l)=Z*(“*v(t)+e.*rand()*(PBest(t)一Present(t))
+e:*rand()*(gBest(t)一Present(t)))
子乍“enr(t+l)=Persent(r)+v(z+1)
来训练最小不确定性神经网络以获得尽可能低的错误分类数目。其中v(O
是粒子t时刻的速度。尸ersent(t)是粒子t时刻的位置值，PBest(t)和gBest(t)
是t时刻粒子的已有个体极值和全局极值。rando是介于【o，l]之间的随机数。
cl，c2是学习因子，通常cl=c2=2。得到的粒子最终训练结果解释为
几一Nlog纸)和鸟一log(
的概率含义即可。上式中参数的设定至
今没有严格的理论依据，所有参数都是根据经验设定的。在后面的试验中
我们设定厂0.9，萨0·8·
单独使用贝叶斯概率或PSO训练最小不确定性神经网各有优缺点。但
二者优缺点具有明显的互补性，且都是针对同一种网络结构—最小不确
定性神经网，这为二者的结合提供了先决条件和实施可能。贝叶斯和PSO
二者结合训练最小不确定性神经网的过程如下:
首先，由贝叶斯概率确定最小不确定性神经网的一组网络权值和闭值。
其次，由这组权值和闽值初始化PSO中的一个粒子，再随机生成或围
绕此粒子生成其它一些粒子。
最后，由PSO方法对这群粒子进行训练，以得到更好的分类结果。
将以上三种方法应用于10种茶味觉信号四的分类识别中(每种茶各100
个样本，共计1000个训练样本)。在信号输入之前我们对二维味觉信号进
行了预处理，根据味觉信号各维的特点，我们将其连续值等距划分在11和
13个离散区域，以适应最小不确定性神经网络离散
Machine vision, hearing, tactual sensation and force sensation are greatly developed in the domain of robotics and some of theirs have been used for practical purposes. Machine taste and smell sensation have wide applications in the intellectualized management in food industries, quality inspection of food, evaluation of taste and smell and so on. However, the progress made in machine taste and smell sensation are far from satisfactory. The most challenging tasks in the domain of machine taste and smell sensation include to construct taste and smell sensors with high sensitivities and to build recognition systems with high correct classification percentages. Many scientists in Japan had pursued their studies on the domain since the 80's of the twentieth century. Nowadays, not only had the basic tastes of sourness, sweetness, bitterness, umami and saltiness been successfully measured, but the quantitive sampling analysis for various foods and beverages, such as coffee, tea, mineral waters and rice, are made c
onsiderable headway.
How to determine the structure and the parameters of the neural networks promptly and efficiently has been a difficult point all the time in the field of neural networks research [47][48]. At present the basic idea to solve this problem is to dig proper information from the data of research, and then guide the construction of neural networks via the previously acquired information, such as successful in constructing neural networks in light of Bayesian Theorem [49] [50]. Optimizing neural networks according to Particle Swarm Optimization (PSO) is newly invented in recent years [51] [52],
A new model of minimal uncertainty neural networks (MUNN) to construct the neural networks is discussed in this paper. It is derived from Minimal Uncertainty Adjudgment to construct the networks structure.
Theorem 1. Let X=(x1,x2...xn) be a N-dimensional input vector, and all attributes x1,x2...xN are separate independent; let P(k) denote the probability of
event k, then is called uncertainty of X to y, and
Corollary 1: When Y={y1,y2...yM) is a classified collection set, the uncertainty of X to yj ( j [1,2...M] ) is determined as:
When classified, choose the minimal
uncertainty j as the finial adjudgment, which is defined as Minimal Uncertainty Adjudgment.
We make the identifications
defined as minimal uncertainty neural networks (MUNN). the
structure of neural networks is determined as shown in Fig. 1. The significations of each layers are as the followings:
Layer[A](input samples): A is the observation set, x ii'is the property of xj,.
Layer[B](weights selection): Where Oii' =1, if xii' A, and Oii'=0,otherwise.
Layer[C](transmited calculation): From Eq. (1) and Eq. (2) we can get Sj.
Layer[D](output uncertainty): Using Eq. (3) to obtain the output of .
Fig. 1. A simply minimal uncertainty neural network with 2 input attributes and 2 classes (N=2).
The MUNN combines with Bayesian Theorem and with Particle Swarm Optimization (PSO) for training.
When determining weights and biases of MUNN by Bayesian Theorem, some counters are calculated first:
where r is the pattern number in the training set, and indicate the presence of in and in is the "strength" of the pattern, typically is 1. Therefore, we deduce:
a is usually very small a number, and in later experiments we assume that a
is 1/C, so the error of the classification is close to log1/C2.
When determining weights and biases of MUNN by PSO, the weights and biases of minimal uncertainty neural networks model can act as the parameters of the particles directly, and the misclassified ones are the fitness values.
Updating particles' velocity and positions with the following formulae:
v(t) is the particle velocity, Persent(t) is the current particle. pBest(t) and gBest(t) are defined as individual best and global best. randQ is a random number between [0 1]. c1, c2 are learning factors. Usually c1 = c2= 2. The final result of
引文
[1] 中野馨：技术评论社，平成3年，pp225-231。
[2] K.Toko,K.Hayashi,M.Yamanaka and K.Yamafuji: Multi-Channel taste sensor with lipid membrance, Tech.Digest, 9th Sensor Symp.,Tokyo,Japan,pp193-196, 1990.
[3] H.Ikezki,K.Toko,K.Hayashi,R.Toukubo,M.Yamanaka,K.Satou and K.Yarnafuji: Intelligent multi-channel taste sensor with Lipid membranes, Tech.Digest,10th Sensor Symp, Tokyo, Japan, 1991, pp173-176.
[4] M.Shimize, Y.Kanai, H.Uchida, C.G.Zhou, H.Maekawa, T.Katsube: Integrated Biosensor Employing A Surface Photo-Voltage Technique. The 7th Intema-tional Conference on Solid-state Sensors and Actuators. pp.495-498, June.1993, Yokohama Japan.
[5] Y.Kanai, M.Shimize, H.Uchida, H.Nakahare, C.G.Zhou, T.Katsube:Integrated Taste Sensor with Surface Photovoltage Technique. The 7th International Conference on Solid state Sensors and Actuators. June.1993, Yokohama Japan, pp.407-410
[6] Y.Kanai, M.Shmizy, H.Uchida, H.Nakahara, C.G.Zhou, H.Maekawa, T.Katsube: Integrated Taste Sensor Using Surface Photo-voltage Technique. Sensors and Actuators, B20, pp.9-13, 1994.
[7] 清水正章，金井康通，内田修和，周春光，胜部昭明：光重合性用表面光检出型硝素试作．CHEMICAL SENSORS．Vol．2，PP．117-120，1994．
[8] Y.Sasaki,Y.Kanai,H.Uchida and T.Katsube: Highly sensitive taste sensor with a new differential LAPS method, Sensors and Actuators B24-25,pp819-822, 1995.
[9] H.Uchida, W.Y.Zhang,and T.Katsube: High speed chemical image sensor with digital LAPS system, Sensors and Actuators B34,ppl-4,1996.
[10] 都甲(氵絜)：味电子情报通信学会志，Vol．80，No．8，pp805-811，1997．
[11] Z.Wenyi,H.Hatakeyama,H.Uchida, H.Maekawa,T.Katsube: Integrated taste sensor using a semiconductor ion sensor, T.IEE Japan Vol.117-E,No.6, pp326-331,1997.
[12] 池崎秀和，谷口晃，都甲(氵絜)脂质膜味定量化，日本化学研究会，CS-98-1-7,pp11-16，1998．
[13] Takahiro Uchida, Yohko Miyanaga, Hiromi Tanaka, Koichi Wada, Seisuke Kurosaki, Toshimitsu Ohki, Makiko Yoshida, and Kenji Matsuyama. Quantitative Evaluation of the Bitterness of Commercial Medicines Using a Taste Sensor. Chem.Pharm.Bull. 48(11) 1843-1845,2000
[14] Ronggang Chen, Masaaki Habara and Kiyoshi Toko. Study of Saltiness Using Taste Sensor with Different Lipid/Polymer Membranes. Sensors and Materials, Vol. 15, No. 3(2003), 155-163.
[15] 王平，陈裕泉，吴坚，束炎，(1996)，人工嗅觉-电子鼻的研究，《中国生物医学工程学报》，V15，N4，344-353，(EI收录，被引用)；
[16] 李蓉，王平，张钦涛，李全政，(2000)一种新型生物化学图象传感器的研究，《中国生物医学工程学报》，V19，N4，382-386，(EI收录)；
[17] H.Yamada, Y.Mizota, K.Toko and T.Doi: Highly Sensitive Discrimination of Taste of Milk with Homogenization Treatment Using Taste Sensor, Materials Science & Engineering, Vol.C5, pp.41-45,1997.
[18] 饭山，池田，都甲，八寻：味觉用酱油味评价，日本食品科学工学会志，Vol．44，pp615-622，1997．
[19] 池崎，谷口，都甲：味用绿茶口味定量化，电气学会论文志E，Vol．117E，No．9，pp465-470,1997．
[20] 江崎，都甲，津田，中谷：味觉味质成分分析，电气学会论文志E，Vol．117E,No．9,pp449-455,1997．
[21] 八寻美希，都甲(氵絜)饭山悟：味觉用米味识别，电气学会论文志E，Vol．117E,No．4,pp187-193，1997．
[22] 都甲(氵絜)味用食品医药品味计测，Vol．32 pp229-238，1998．
[23] 安彦刚志，渡边俊一郎，张文艺，内田秀和，胜部昭明：
用高安定茶味，日本化学研究会，CS-98-1-7,pp17-21，1998．
[24] Masaaki Habara and Kiyoshi TOKO. Discrimination of Saltiness with Coexisting Components Using Multichannel Taste Sensor with Lipid Membranes. IEICE TRANS. ELECTRON, VOL. E83-C, NO.7 JULY 2000.
[25] Hirotaka Kaneda, Naoyuki Kobayashi, Junji Watari, Ken Shinotsuka, Masachika Takashio, and Yoshio Okahata. A New Taste Sensor for Evaluation of Beer Body and Smoothness Using a Lipid-Coated Quartz Crystal Microbalance. American Society of Brewing Chemists. 60(2): 71-76, 2002
[26] Maxsim Yap Mee Sim, Teo Jau Shya, Mohd Noor Ahmad, Ali Yeon Md Shakaff, Abdul Rahman Othman and Muhammad Suzuri Hitam. Monitoring of Milk Quality with Disposable Taste Sensor. Sensors 2003, 3, 340-349. pp181-186,1992.
[27] 周春光，胜部昭明，神经网络味觉信号的学习和识别．吉林大学自然科学学报．No．1，pp．31-34，1994．
[28] 周春光，味觉信号的特征抽取．吉林大学自然科学学报．No．2，pp．25-28，1994．
[29] Li Rong, Wang Ping, Hu Wenlei, (2000), A novel method for wine analysis based on sensor fusion technology, Sensors & Actuators B, B66: 246-250. (SCI收录，EI收录，被引用)；
[30] 李蓉，吴一聪，严伟民，王平，郑筱祥，(2002)，新型细胞微生理计及其在药物筛选中的应用，《中国生物医学工程学报》，V15，N4，344-353，(EI收录)；
[31] 黄艳新，周春光，杨国慧，邹淑雪。基于熵聚类模糊神经网络味觉信号识别的研究，计算机研究与发展，2004，vol 41，No．3，pp414-419．
[32] 黄艳新，于哲舟，胡成全，邹淑雪，周春光。基于粗糙集方法的模糊神 经网络味觉信号识别系统研究，吉林大学学报(信息科学版)，2004，Vol．20No．3，pp??-??。(待定，5月刊出)
[33] 横山圣，内田秀和，张文艺，胜部昭明：味觉基本味定量评价，日本化学研究会，CS-99-43-58,pp7-10，1999．
[34] 周春光，梁艳春等著，《计算智能》：吉林大学出版社，2001年11月第一版。
[35] P. SALEK*, J. TARASIUK, K. WIERZBANOWSKI. Application of Genetic Algorithms to Texture Analysis. Cryst.Res.Technol Vol.34, 1999, NO.8: pp 1073-1079
[36] D. G. Stork, G. Wolff, and E. Levine, "A neural network lipreading system for improved speech recognition," in Proc. of Int. Joint Conf. on Neural Networks, 1992, pp. 285—295.
[37] T.nakamoto,H.takagi,S.Utsumi and T.Moritzumi: Gas/Odor dentification by semiconductor gas sensor array and an analog neural network circuit, Sensors and Actuators, B8, pp 181-186, 1992.
[38] Hao Bo,Hitoshi Maekawa, Yutaka Sasaki,Hidekazu Uchida and Teruaki Katsube: Feature Extraction for Taste Sensor Signal Processing by Neural Network,TECHNICAL REPORT OF IEICE, CPM94-34,Ome94-29,pp34-40,1994.
[39] 周春光，张冰，程彦丰，胡成全：遗传算法在训练前向神经网络中的应用．小型微型计算机系统．Vol．17，No．9，pp．54-58，1996．
[40] 周春光，周国芹，程彦丰，梁艳春：一种快速收敛的遗传算法．软件学报．Vol.7, Supplement, pp.311-314, 1996.
[41] 周春光，周国芹，程彦丰，常迪，梁艳春：一种克服遗传算法收敛于局部极小的方法．小型微型计算机系统．Vol．18，No．3，pp．46-49，1997．
[42] 田勇，周春光，梁艳春：基于模糊神经网络味觉信号的识别研究．计算机应用．No．1，pp．42-48，1998．
[43] 周春光，梁艳春，田勇，胡成全，孙新：基于模糊神经网络味觉信号识别的研究．计算机研究与发展．Vol．36，No．4，pp401-409，Apr．1999．
[44] 周春光：味觉信号的特征抽取．吉林大学自然科学学报．No．2，pp．25-28，1994．
[45] Wang Ping, Xie Jun, (1996), The Recognition Method Combined Neural Network with Fuzzy Logic for Odor Recognition, Meas. Sci. & Tech. 7/12, 1707-1712, (SCI、EI收录，被引用)；
[46] 周春光，梁艳春，田勇，胡成全，孙新：基于模糊神经网络味觉信号识别的研究．计算机研究与发展．Vol．36,No．4，pp401—409,Apr．1999．
[47] ZHOU Chun-Guang,LIANG Yan-Chun,TIAN Yong,HU Cheng-Quan and SUN Xi. A Study of Identification of Taste Signals Based on Fuzzy Neural Networks. Journal of Computer Research & Development(in Chinese),Vol.36.No.4.Apr. 1999: 401～409(周春光，梁艳春，田勇，胡成全，孙新．基于模糊神经网络味觉信号识别的研究．计算机研究与发展，Vol．36．No．4．Apr．1999：401～409)
[48] Johansen, M. M. Evolving Neural Networks for Classification. Topics of Evolutionary Computation 2002,Collection of Student Reports: 57～63
[49] Kochi,India. Ninan Sajeeth Philip and K.Babu Joseph. Boosting the Differences:A Fast Bayesian Classifier Neural Network. Intelligent Data Analysis, 4 (2000), IOS press, Netherlands, 2000: 463～473
[50] Matthew A.Kupinski,Darrin C.Edwards,Maryellen L.Giger and Charles E.Metz. Ideal Observer Approximation Using Bayesian Classification Neural Networks. IEEE Transactions On Medical Imaging, Vol.20,No.9,Sep.2001:886～899
[51] Jakob Vesterstrom and Jacques Riget. Particle Swarms-Extensions for improved local,multi-modal,and dynamic search in numerical optimization. [master thesis]. EVALife Group,Department of Computer Science Ny Munkegade,Bldg,540,University of Aarhus DK-800 Aarhus C.Denmark,May 2002.
[52] Settles, M. and Rylander, B. Neural network learning using particle swarm optimizers. Advances in Information Science and Soft Computing, 2002:224～226
[53] Shunichiro Watanabe,Akira Yokoyama,Zhang Wenyi,Takeshi Abiko,Hidekazu Uchida, Teruaki Katsube. Detection mechanism of taste signals with commercial ion sensors. Saitama University, The journal of the Institute of Electrical Engineers of Japan (in Japanese). Vol.CS-98-30,1998.7:13～18
Vol.CS-98-30,1998.7:13～18)
[54] Zhou Chun-Guang,Liang Yan-Chun. Computational Intelligence. ChangChun:JiLin University Press,2001(周春光，梁艳春等著，《计算智能》：吉林大学出版社，2001年11月)
[55] Stockholm,Sweden. Ander Holst,Dissertation. The Use of a Bayesian Neural Network Model for Classification Tasks. [PhD dissertation]. Department of Numerical Analysis and Computing Science,Royal Institute of Technology, September 1997.
[56] J.Kennedy and R.C.Eberhart. Particle swarm optimization. Proc.IEEE int'l conf.on neural networks Vol.Ⅳ, IEEE service center, Piscataway, NJ,1995:1942～1948